Extension of Metabolic Control Analysis and Biochemical Systems Theory to Stochastic Systems

该项目的目标是发展随机生化反应系统的摄动分析理论，并利用该理论揭示各种生物网络基序的随机特性。细胞过程是由相互作用的蛋白质、基因和小分子网络控制的。传统上，这样的系统用连续统/确定性模型来描述，通常基于微分方程。在这些模型中，假定各种分子种类的浓度可以用连续变量来描述。在许多情况下，这是相当合理的，因为任何特定物种的分子数量都可以很大。然而，有一些细胞子系统，如基因网络，其中的分子数量可能只有几个。在这样的系统中，连续模型是不合适的。此外，由于分子数如此之小，化学过程的随机性成为一个主要特征。在这个项目中，确定性理论将被重新表述，以发展生化网络中噪声传播的一般分析理论。该项目将使用该理论来理解不同网络基元的随机特性，并做出可以通过实验验证的预测。生物细胞包含数百万个随机碰撞和反应的分子。所有这些活动的净影响是噪音，称为随机噪音。电气工程师不得不一直处理电子电路中不必要的噪音，他们付出了巨大的努力来消除它。实验上，细胞中的噪声可以测量，但缺乏的是对这种噪声在如此复杂的系统中如何表现的理解。如果噪音能被更好地理解，工程师就能更好地控制它。这个项目将发展一种数学理论，使科学家和工程师能够理解和预测噪音是如何在细胞内传播的。这个项目涉及许多科学领域，包括分子生物学、计算机科学、控制理论、信号处理和电路理论。本科生和研究生将参与该项目，他们将接受多学科科学的培训。

The objective of this project is to develop a theory of perturbation analysis for stochastic biochemical reaction systems and to use this theory to uncover the stochastic properties of a variety of biological network motifs. Cellular processes are controlled by networks of interacting proteins, genes and small molecules. Traditionally such systems have been described using a continuum/deterministic model, often based on differential equations. In these models it is assumed that the concentrations of the various molecular species can be described using continuous variables. In a number of cases this is quite reasonable because the number of molecules of any particular species can be large. However there are some cellular subsystems, such as gene networks, where the number of molecules might be as low as a few. In such systems a continuous model is inappropriate. Moreover, because the molecular numbers are so small, the stochastic nature of chemical processes becomes a dominant feature. In this project the deterministic theory will be reformulated in order to develop a general analytical theory of noise propagation in biochemical networks. The project will use the theory to understand the stochastic properties of different network motifs and to make predictions which can be tested experimentally. Biological cells contain millions of molecules randomly colliding and reacting. The net effect of all this activity is noise, called stochastic noise. Electrical engineers have to deal with unwanted noise in electronic circuits all the time and they go to great efforts to eliminate it. Experimentally, noise in cells can be measured but what is lacking is an understanding of how this noise behaves in such complicated systems. If noise could be better understood, engineers would be in a better position to control it. This project will develop a mathematical theory that will allow scientists and engineers to understand and predict how noise spreads inside a cell. This project impinges on many areas of science, including molecular biology, computer science, control theory, signal processing and electrical circuit theory. Undergraduate and graduate students will participate in this project and they will be trained in multidisciplinary science.